Determination of EOQ in terms of optimum degrees of horizontal and vertical cooperation at a node of supply chain

In a complex supply chain network, the production nodes, seller nodes, and buyers are connected randomly. We assume a process of joining two random nodes leading to the bivariate Poisson probability mass function. There exist two types of links- one is horizontal (H) and the other is vertical (V), which support the continuous flow of commodities through the supply chain. This induces competition among workers at a node to manage these two types of links within fixed constraints and creates bargaining to decide the optimal degree of both types of links at a node. We use the Nash security point to obtain the bargaining solution describing the optimal links. We reduce the carrying cost and ordering cost of inventory, which are contrary in their nature by introducing horizontal and vertical links, respectively. We modify the total cost function and establish a new economic order quantity (EOQ), optimal shortage quantity, and total optimal cost in terms of the optimal degree of H and V cooperation.